Natural ultrabornological, non-complete, normed function spaces
type: Item
instance of: scholarly article
title: Natural ultrabornological, non-complete, normed function spaces
zbMATH Open document ID: 0783.46003
DOI: 10.1007/BF01207546
author: Antonio Gilioli
published in: Archiv der Mathematik
publication date: 1994-03-17T00:00:00Z
review text: Using a method with a family of projections \((P_ \lambda)_{\lambda\in[a,b]}\) it is proved that certain subspaces of Fréchet spaces are ultrabornological. It turns out that many elementary spaces of classical analysis, which are non-complete subspaces of the space of continuous functions on \([a,b]\) with values in a Banach space, are ultrabornological. In particular, the space of Denjoy-Perron- Kurzweil-Henstock-integrable functions, under the Alexiewicz norm, is ultrabornological. These new examples of non-complete, normed ultrabornological spaces seem to be the simplest ones known so far.
Mathematics Subject Classification ID: 46A08
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 493373
zbMATH Keywords: subspaces of Fréchet spaces
zbMATH Keywords: ultrabornological
zbMATH Keywords: space of Denjoy-Perron- Kurzweil-Henstock-integrable functions
zbMATH Keywords: Alexiewicz norm
zbMATH Keywords: examples of non- complete, normed ultrabornological spaces
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01207546
OpenAlex ID: W2091180408
description: scientific article; zbMATH DE number 493373